Kepler’s lawsKepler’s laws

Ancient Astronomy

• Ancient civilizations observed the skies

• Many built structures to mark astronomical events for religious and practical reasons: Seasons, day light gain and loss etc

Summer solstice sunrise at Stonehenge

(2800B.C. till 1100B.C)

Big Horn Medicine in Wyoming

Spokes of the Big Horn Medicine Wheel are aligned with rising and setting of Sun and other stars

Features that align with rising and setting of the sun and other stars.

Caracol temple in Mexico

This temple at Caracol, in Mexico, has many windows that are aligned with astronomical events:

Keeping track of the seasons

The Geocentric Universe

Aristotle (384-322 B.C.)Ancient astronomers observed:

Sun

Moon

Stars

Five planets: Mercury, Venus, Mars, Jupiter, Saturn

Sun, Moon, and stars all have simple movements in the sky

Planets motion are more complicated:

• Move with respect to fixed stars

• Change in brightness

• Change speed

• Undergo retrograde motion

• Inferior planets: Mercury, Venus

• Superior planets: Mars, Jupiter, Saturn

Now know:

Inferior planets have orbits closer to Sun than Earth’s

Superior planets’ orbits are farther away

The Geocentric Universe

Earliest models had Earth at center of solar system

Needed lots of complications to accurately track planetary motions

Cosmic lecture launcher:3.15 Ptolemy’s model

The scientific methodThe scientific method

• New observations (retrograde New observations (retrograde motion, phases of Venus) lead to new motion, phases of Venus) lead to new model:model:

Heliocentric universeHeliocentric universe

• Heliocentric universe allows for new Heliocentric universe allows for new predictions: Phases and retrograde predictions: Phases and retrograde motion of other planets motion of other planets

The Foundations of the Copernican Revolution (1473-1543)

1. Earth is not at the center of everything.

2. Center of earth is the center of moon’s orbit.

3. All planets revolve around the Sun.

4. The stars are very much farther away than the Sun.

5. The apparent movement of the stars around the Earth is due to the Earth’s rotation.

6. The apparent movement of the Sun around the Earth is due to the Earth’s rotation.

7. Retrograde motion of planets is due to Earth’s motion around the Sun.

Kepler’s Laws of Planetary Motion

Kepler’s laws were derived using observations made by Tycho Brahe(1546-1601)

Kepler: 1571-1630 AC

Kepler’s 1’st law

First Law: Planetary orbits are ellipses (not circular), Sun at one focus

Cosmic lecture launcher:

Drawing an ellipse.

Some Properties of Planetary Orbits

Semimajor axis and eccentricity of orbit completely describe it

Perihelion: closest approach to Sun

Aphelion: farthest distance from Sun

x

a

c

e=c/aCircle: c=0, e=0

1) planets orbit the Sun.

2) orbits are noncircular.

3) orbits are elliptical in shape.

4) all of the above

Question

Kepler’s 1st law of planetary orbits states that

1) planets orbit the Sun.

2) orbits are noncircular.

3) orbits are elliptical in shape.

4) all of the above

Question

Kepler’s 1st law of planetary orbits states that

Kepler’s Laws apply to all orbiting objects. The Moon orbits Earth in an ellipse, and the Space Shuttle orbits Earth in an ellipse, too.

Kepler’s 2’nd law

Second Law: Imaginary line connecting Sun and planet sweeps out equal areas in equal times

1

234

5

6

Areas:

Area A= Area B

= Area C

Times:

t2-t1=t4-t3=t6-t1

Distance traveled:

d12 > d34>d56

Question

Earth is closer to the Sun in January. From this fact, Kepler’s 2nd law tells us

1) Earth orbits slower in January.

2) Earth orbits faster in January.

3) Earth’s orbital speed doesn’t change.

Earth is closer to the Sun in January. From this fact, Kepler’s 2nd law tells us

1) Earth orbits slower in January.

2) Earth orbits faster in January.

3) Earth’s orbital speed doesn’t change.

Kepler’s 2nd law means that a planet moves faster when closer to the star.

Faster

Slower

Question

Kepler’s 3’rd law

Third Law: Square of period of planet’s orbital motion is proportional to cube of semimajor axis:

Orbits must be given in AU

and periods in

Earth years!

13

232

a

PaP

Question

Kepler’s 3rd law relates a planet’s distance from the Sun and its orbital

1) speed.

2) period.

3) shape.

4) velocity.

Kepler’s 3rd law relates a planet’s distance from the Sun and its orbital

1) speed.

2) period.

3) shape.

4) velocity.

Kepler’s 3rd law P2 = a3

means more distant planets orbit more slowly.

Question 13

Venus’ Period = 225 days

Venus’ axis = 0.7 AU

Earth’s Period = 365 days

Earth’s axis = 1.0 AU

The Dimensions of the Solar System

Now measured using radar:

Ratio of mean radius of Venus’s orbit to that of Earth very well known